In today's business and scientific world, color has become essential as a component of communication. Color facilitates the sharing of knowledge and ideas. Companies involved in the development of digital color print engines are continuously looking for ways to improve the total image quality of their products. One of the elements that affects image quality is the ability to consistently produce the same quality image output on a printer from one day to another, from one week to the next, month after month. Colors on a printer tend to drift over time due to ink/toner variations, temperature fluctuations, type of media used, environment, etc. There has been a long felt commercial need for efficiently maintaining print color predictability, particularly as electronic marketing has placed more importance on the accurate representation of merchandise in illustrative print or display media.
Color printing characterization is a crucial task in color management. The characterization process essentially establishes a relationship between device dependent, e.g. printer CMY, and device independent, e.g. CIELAB values. Several color management tasks such as derivation of ICC profiles, color transforms for calibration, etc. benefit from an accurate mathematical characterization of the physical device. For color printers, characterization is an expensive process involving large numbers of patch measurements and subsequent computation to derive satisfactorily accurate color lookup-tables (LUTs).
Color printer characterization is the process of deriving a mathematical transform which relates printer color CMY(K) to its corresponding device independent representation, e.g. spectral color, CIELAB, etc. The forward characterization transform defines the response of the device to a known input thus describing the color characteristics of the device. The inverse characterization transform compensates for these characteristics and determines the input to the device that is required to obtain a desired response. For the printers hence, a CMY(K)→CIELAB mapping represents a forward characterization transform while the CIELAB→CMY(K) map is an inverse transform. Herein the characterization color transform will be used to refer unambiguously to the forward transform; suitable inversion methods can be used to derive the corresponding inverse transform. The characterization transform is of immense value in many color management tasks such as derivation of ICC profiles for the printer, printer calibration, color control, etc.
To ensure accurate color reproduction for printers, characterization and calibration processes are required. The characterization procedure is often performed in-factory to create machine profiles, while the calibration procedure, which updates the profiles, may be performed in-factory by the manufacturers, or at the customer-site by users. During printer characterization and calibration, color patches are printed and measured, and the machine characteristics are determined by comparing the desired outputs and the actual measured data. In order to precisely measure the color covering the entire printer gamut, the conventional characterization and calibration processes apply a large number of color patches. The number of patches increases drastically if calibrations for multiple media, UCR/GCR strategies, and/or halftone schemes are required.
As the number of color patches is a decisive factor for characterization/calibration cost and time needed, several different methods have been proposed to reduce the number of color patches. One of such approaches is to replace the multi-dimensional (M>=3) LUT by two-dimensional look-up tables instead. Because the two dimensional LUTs are by construction smaller than three or four dimensional LUTs for example, a patch reduction is obtained but at the cost of color accuracy. For example, a multi-dimensional matrix representation of the LUT, can be approximated by decomposition of the multi-dimensional matrix into smaller matrices. In a Principal Component Analysis (PCA) based approach, the color mapping function is modeled as a linear combination of a set of eigen functions. The method may drastically reduce the patches required during calibration, but its characterization process is far more complicated and still needs patches proportional to the number of nodes in the multi-dimensional LUT.
In a radically different approach Wang et al. propose a halftone independent binary printer model to obtain characterization LUTs. S. Wang, et al., U.S. Pat. No. 5,469,267, U.S. Pat. No. 5,748,330, U.S. Pat. No. 5,854,882, U.S. Pat. No. 6,266,157, and U.S. Pat. No. 6,435,654. This approach has a powerful advantage of not repeating patch measurements as a function of halftone. However, its accuracy in predicting measured color needs improvement.
It would be advantageous, and thus there is a need, to interpret multi-dimensional LUTs as tensors and apply tensor decompositions such as parallel-factor analysis to obtain compact representations of LUTs. From a mathematical viewpoint, tensor decompositions naturally unearth structure in multi-dimensional LUTs which is otherwise hard to predict. Hence, whenever a compact representation of a multi-dimensional LUT/tensor is possible via parallel factors it is equivalently possible to derive/represent the LUT with reduced effort in the sense of storage, computation and/or measurement.